Retorno e previsões

Log de Retornos

Carregamos os dados:

Visualizando os dados dos nossos últimos retornos dos preços, temos:

Modelagem com fpp3 e validação cruzada temporal

Precisaremos fazer um forecasting de curto prazo com nossos dados históricos de retornos pra formularmos nossas recomendações posteriores de compra, venda e espera:

Vamos começar com uma série por vez $\Rightarrow$ SAP

War models

Selecionamos o melhor modelo (1 fold de validação cruzada somente):

Gero um cenário com o modelo:

Plotamos os forecasts com esse modelo pra três cenários distintos no futuro:

--- title: "Retorno e previsões" format: html: self-contained: true toc: true code-tools: true code-fold: true df-print: paged css: - styles.css - https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.1.1/css/all.min.css extensions: [fontawesome] editor: visual --- <div> ## Log de Retornos ```{r setup, include=FALSE} knitr::opts_chunk$set( message = FALSE, warning = FALSE, comment = NA, include = FALSE ) knitr::opts_chunk$set(comment = NA) # Remove all coments # of R outputs knitr::opts_chunk$set(warning = FALSE) # Remove all warnings # of R outputs knitr::opts_chunk$set(message = FALSE) # Remove all messages # of R outputs ``` ```{r} #| include: false library(tidyverse) library(tidymodels) library(modeltime) library(timetk) library(purrr) library(tidyquant) library(tsibble) library(prophet) library(feasts) library(fable) library(fabletools) library(lubridate) library(tictoc) ``` Carregamos os dados: ```{r} #| include: false tickers <- c( "SAP", "CRM", "NOW", "ORCL", "IBM", "MSFT" ) ``` ```{r} #| include: false portfolioPrices <- NULL for ( Ticker in tickers ) portfolioPrices <- cbind( portfolioPrices, quantmod::getSymbols.yahoo( Ticker, from = "2019-01-01", auto.assign = FALSE )[,4] ) portfolioPrices <- portfolioPrices[apply(portfolioPrices, 1, function(x) all(!is.na(x))),] colnames(portfolioPrices) <- c( "SAP", "CRM", "NOW", "ORCL", "IBM", "MSFT" ) # Visualizar com DT #DT::datatable(tail(portfolioPrices), options = list(pageLength = 10, scrollX = TRUE)) ``` Visualizando os dados dos nossos últimos retornos dos preços, temos: ```{r fig.height=9, fig.width=9} #| echo: false log_returns <- log(portfolioPrices) - log(lag(portfolioPrices)) log_returns <- na.omit(log_returns) log_returns <- log_returns |> timetk::tk_tbl(preserve_index = TRUE, rename_index = "date") tail(log_returns) ``` ```{r fig.height=9, fig.width=9} #| echo: false ln_returns <- log_returns ln_returns |> as.data.frame() |> dplyr::mutate( time = seq_along( SAP ) ) |> select(-date) |> tidyr::pivot_longer( !time, names_to = "Variables", values_to = "Value" ) |> dplyr::group_by(Variables) |> timetk::plot_time_series( time, Value, .interactive = F, # Change for TRUE for better visualization .facet_ncol = 2, .smooth = FALSE ) + ggplot2::theme( strip.background = ggplot2::element_rect(fill = "white", colour = "white") ) ``` ### Modelagem com fpp3 e validação cruzada temporal Precisaremos fazer um forecasting de curto prazo com nossos dados históricos de retornos pra formularmos nossas recomendações posteriores de compra, venda e espera: - Vamos começar com uma série por vez $\Rightarrow$ SAP ```{r} #| include: false # Primeiro converto pra tsibble lnretSAP <- log_returns |> select(date, SAP) |> as_tsibble(index = date) glimpse(lnretSAP) ``` ```{r} #| include: false treino <- lnretSAP |> filter_index(~"2025-01-01") ``` War models ```{r} #| include: false tic() Modelos <- treino |> model( AjusteExp = ETS(SAP ~ error("A") + trend("N") + season("N")), # Ajuste Exponencial com auto AjExp_aditivo = ETS(SAP ~ error("A") + trend("A") + season("A")), # Ajuste Exponencial Aditivo AjExp_multiplicativo = ETS(SAP ~ error("M") + trend("A") + season("M")), # Ajuste Exponencial Multiplicativo Croston = CROSTON(SAP), # Modelo Croston HoltWinters = ETS(SAP ~ error("M") + trend("Ad") + season("M")), # Holt Winters Holt = ETS(SAP ~ error("A") + trend("A") + season("N")), # Holt HoltAmort = ETS(SAP ~ error("A") + trend("Ad", phi = 0.9) + season("N")), # Holt Amortecida Regr_Comp = TSLM(SAP ~ trend() + season()), # Regressao com tendencia e sazonalidade auto Regr_Harmonica = TSLM(SAP ~ trend() + fourier(K = 2)), # Regressao harmonica Regr_Quebras = TSLM(SAP ~ trend(knots = c(2018, 2019, 2020))), # Regressao com quebras estruturais Snaive = SNAIVE(SAP), # SNAIVE Naive = NAIVE(SAP), #NAIVE Media_Movel = ARIMA(SAP ~ pdq(0,0,1)), # Media Movel Simples autoARIMA = ARIMA(SAP, stepwise = FALSE, approx = FALSE), # Auto ARIMA autoARIMA_saz = ARIMA(SAP, stepwise = FALSE, approx = FALSE, seasonal = TRUE), # AutoARIMA Sazonal # Regr_erros_ARIMA = auto.arima(SAP, xreg = fourier(K = 3), seasonal = FALSE), # Regressao com erros ARIMA ARIMA_saz_012011 = ARIMA(SAP ~ pdq(0,1,2) + PDQ(0,1,1)), # ARIMA Sazonal ordem 012011 ARIMA_saz_210011 = ARIMA(SAP ~ pdq(2,1,0) + PDQ(0,1,1)), # ARIMA Sazonal ordem 210011 ARIMA_saz_0301012 = ARIMA(SAP ~ 0 + pdq(3,0,1) + PDQ(0,1,2)), # ARIMA sazonal ARIMA_quad = ARIMA(SAP ~ I(trend()^2)), # ARIMA com tendencia temporal quadratica ARIMA_determ = ARIMA(SAP ~ 1 + trend() + pdq(d = 0)), # ARIMA com tendencia deterministica ARIMA_estocastico = ARIMA(SAP ~ pdq(d = 1)), # ARIMA com tendência estocastica Regr_Harm_dinamica = ARIMA(SAP ~ fourier(K=2) + PDQ(0,0,0)), # Regressao Harmonica Dinamica Regr_Harm_Din_MultSaz = ARIMA(SAP ~ PDQ(0, 0, 0) + pdq(d = 0) + fourier(period = 7*30, K = 10) + fourier(period = 7*30, K = 5)), Regr_Harm_Din_Saz = ARIMA(SAP ~ PDQ(0, 0, 0) + pdq(d = 0) + fourier(period = "month", K = 10) + fourier(period = "year", K = 2) ), # Rgr Harm Mult Saz Complexa # Auto_Prophet = prophet(SAP), # Auto prophet # Prophet_mult = prophet(SAP ~ season(period = "month", order = 2, type = "multiplicative")), # Prophet_aditivo = prophet(SAP ~ season(period = "month", order = 2, type = "additive")), # Prophet_geom = prophet(SAP ~ growth("geometric") + season(period = "month", order = 2, type = "multiplicative")), # Prophet_memo = prophet(SAP ~ growth("geometric") + season(period = "month", order = 5) + # season(period = "year", order = 2, type = "multiplicative")), Modelo_VAR = VAR(SAP, ic = "bic"), # Vetor Autoregressivo Random_Walk = RW(SAP ~ drift()), # Random Walk com drift Rede_Neural_AR = NNETAR(SAP, bootstrap = TRUE)#, # Rede Neural com auto AR e bootstraping nos erros # x11 = X_13ARIMA_SEATS(SAP ~ x11()) # X11 ARIMA Seats ) |> forecast(h = "24 months") # Horizonte de projecao para os proximos 30 dias apos corte no treino toc() ``` Selecionamos o melhor modelo (1 fold de validação cruzada somente): ```{r} #| echo: false Modelos |> accuracy(lnretSAP) |> arrange(RMSE) # Seleção da acuracia pelo menor RMSE para o conjunto de modelos ``` Gero um cenário com o modelo: ```{r} #| include: false fit <- lnretSAP |> model( Regr_Quebras = TSLM(SAP ~ trend(knots = c(2018, 2019, 2020))), # Regressao com quebras estruturais ) sim <- fit |> generate(h = 30, times = 5, bootstrap = TRUE) ``` Plotamos os forecasts com esse modelo pra três cenários distintos no futuro: ```{r fig.height=4, fig.width=9} #| echo: false lnretSAP |> filter_index("2025-01-01"~.) |> ggplot(aes(x = date)) + geom_line(aes(y = SAP)) + geom_line(aes(y = .sim, colour = as.factor(.rep)), data = sim) + labs(title="Valores projetados de retornos de preços de contratos futuros da SAP", y="$US" ) + guides(colour = "none") ``` ```{r} #| include: false # Primeiro converto pra tsibble lnretCRM <- log_returns |> select(date, CRM) |> as_tsibble(index = date) glimpse(lnretCRM) ``` ```{r} #| include: false treino <- lnretCRM |> filter_index(~"2025-01-01") ``` ```{r} #| include: false tic() Modelos <- treino |> model( AjusteExp = ETS(CRM ~ error("A") + trend("N") + season("N")), # Ajuste Exponencial com auto AjExp_aditivo = ETS(CRM ~ error("A") + trend("A") + season("A")), # Ajuste Exponencial Aditivo AjExp_multiplicativo = ETS(CRM ~ error("M") + trend("A") + season("M")), # Ajuste Exponencial Multiplicativo Croston = CROSTON(CRM), # Modelo Croston HoltWinters = ETS(CRM ~ error("M") + trend("Ad") + season("M")), # Holt Winters Holt = ETS(CRM ~ error("A") + trend("A") + season("N")), # Holt HoltAmort = ETS(CRM ~ error("A") + trend("Ad", phi = 0.9) + season("N")), # Holt Amortecida Regr_Comp = TSLM(CRM ~ trend() + season()), # Regressao com tendencia e sazonalidade auto Regr_Harmonica = TSLM(CRM ~ trend() + fourier(K = 2)), # Regressao harmonica Regr_Quebras = TSLM(CRM ~ trend(knots = c(2018, 2019, 2020))), # Regressao com quebras estruturais Snaive = SNAIVE(CRM), # SNAIVE Naive = NAIVE(CRM), #NAIVE Media_Movel = ARIMA(CRM ~ pdq(0,0,1)), # Media Movel Simples autoARIMA = ARIMA(CRM, stepwise = FALSE, approx = FALSE), # Auto ARIMA autoARIMA_saz = ARIMA(CRM, stepwise = FALSE, approx = FALSE, seasonal = TRUE), # AutoARIMA Sazonal # Regr_erros_ARIMA = auto.arima(SAP, xreg = fourier(K = 3), seasonal = FALSE), # Regressao com erros ARIMA ARIMA_saz_012011 = ARIMA(CRM ~ pdq(0,1,2) + PDQ(0,1,1)), # ARIMA Sazonal ordem 012011 ARIMA_saz_210011 = ARIMA(CRM ~ pdq(2,1,0) + PDQ(0,1,1)), # ARIMA Sazonal ordem 210011 ARIMA_saz_0301012 = ARIMA(CRM ~ 0 + pdq(3,0,1) + PDQ(0,1,2)), # ARIMA sazonal ARIMA_quad = ARIMA(CRM ~ I(trend()^2)), # ARIMA com tendencia temporal quadratica ARIMA_determ = ARIMA(CRM ~ 1 + trend() + pdq(d = 0)), # ARIMA com tendencia deterministica ARIMA_estocastico = ARIMA(CRM ~ pdq(d = 1)), # ARIMA com tendência estocastica Regr_Harm_dinamica = ARIMA(CRM ~ fourier(K=2) + PDQ(0,0,0)), # Regressao Harmonica Dinamica Regr_Harm_Din_MultSaz = ARIMA(CRM ~ PDQ(0, 0, 0) + pdq(d = 0) + fourier(period = 7*30, K = 10) + fourier(period = 7*30, K = 5)), Regr_Harm_Din_Saz = ARIMA(CRM ~ PDQ(0, 0, 0) + pdq(d = 0) + fourier(period = "month", K = 10) + fourier(period = "year", K = 2) ), # Rgr Harm Mult Saz Complexa # Auto_Prophet = prophet(SAP), # Auto prophet # Prophet_mult = prophet(SAP ~ season(period = "month", order = 2, type = "multiplicative")), # Prophet_aditivo = prophet(SAP ~ season(period = "month", order = 2, type = "additive")), # Prophet_geom = prophet(SAP ~ growth("geometric") + season(period = "month", order = 2, type = "multiplicative")), # Prophet_memo = prophet(SAP ~ growth("geometric") + season(period = "month", order = 5) + # season(period = "year", order = 2, type = "multiplicative")), Modelo_VAR = VAR(CRM, ic = "bic"), # Vetor Autoregressivo Random_Walk = RW(CRM ~ drift()), # Random Walk com drift Rede_Neural_AR = NNETAR(CRM, bootstrap = TRUE)#, # Rede Neural com auto AR e bootstraping nos erros # x11 = X_13ARIMA_SEATS(SAP ~ x11()) # X11 ARIMA Seats ) |> forecast(h = "24 months") # Horizonte de projecao para os proximos 30 dias apos corte no treino toc() ``` ```{r} #| include: false fit <- lnretCRM |> model( Regr_Quebras = TSLM(CRM ~ trend(knots = c(2018, 2019, 2020))), # Regressao com quebras estruturais ) sim <- fit |> generate(h = 30, times = 5, bootstrap = TRUE) ``` ```{r fig.height=4, fig.width=9} #| echo: false lnretCRM |> filter_index("2025-01-01"~.) |> ggplot(aes(x = date)) + geom_line(aes(y = CRM)) + geom_line(aes(y = .sim, colour = as.factor(.rep)), data = sim) + labs(title="Valores projetados de retornos de preços de contratos futuros da SALESFORCE", y="$US" ) + guides(colour = "none") ``` </div> ```{r fig.align='center', fig.height=3.5, fig.width=9} #| echo: false # Processamento para NOW lnretNOW <- log_returns |> select(date, NOW) |> as_tsibble(index = date) treino <- lnretNOW |> filter_index(~"2025-01-01") # Modelagem tic() Modelos <- treino |> model( AjusteExp = ETS(NOW ~ error("A") + trend("N") + season("N")), AjExp_aditivo = ETS(NOW ~ error("A") + trend("A") + season("A")), AjExp_multiplicativo = ETS(NOW ~ error("M") + trend("A") + season("M")), Croston = CROSTON(NOW), HoltWinters = ETS(NOW ~ error("M") + trend("Ad") + season("M")), Holt = ETS(NOW ~ error("A") + trend("A") + season("N")), HoltAmort = ETS(NOW ~ error("A") + trend("Ad", phi = 0.9) + season("N")), Regr_Comp = TSLM(NOW ~ trend() + season()), Regr_Harmonica = TSLM(NOW ~ trend() + fourier(K = 2)), Regr_Quebras = TSLM(NOW ~ trend(knots = c(2018, 2019, 2020))), Snaive = SNAIVE(NOW), Naive = NAIVE(NOW), Media_Movel = ARIMA(NOW ~ pdq(0,0,1)), autoARIMA = ARIMA(NOW, stepwise = FALSE, approx = FALSE), autoARIMA_saz = ARIMA(NOW, stepwise = FALSE, approx = FALSE, seasonal = TRUE), ARIMA_saz_012011 = ARIMA(NOW ~ pdq(0,1,2) + PDQ(0,1,1)), ARIMA_saz_210011 = ARIMA(NOW ~ pdq(2,1,0) + PDQ(0,1,1)), ARIMA_saz_0301012 = ARIMA(NOW ~ 0 + pdq(3,0,1) + PDQ(0,1,2)), ARIMA_quad = ARIMA(NOW ~ I(trend()^2)), ARIMA_determ = ARIMA(NOW ~ 1 + trend() + pdq(d = 0)), ARIMA_estocastico = ARIMA(NOW ~ pdq(d = 1)), Regr_Harm_dinamica = ARIMA(NOW ~ fourier(K=2) + PDQ(0,0,0)), Regr_Harm_Din_MultSaz = ARIMA(NOW ~ PDQ(0, 0, 0) + pdq(d = 0) + fourier(period = 7*30, K = 10) + fourier(period = 7*30, K = 5)), Regr_Harm_Din_Saz = ARIMA(NOW ~ PDQ(0, 0, 0) + pdq(d = 0) + fourier(period = "month", K = 10) + fourier(period = "year", K = 2)), Modelo_VAR = VAR(NOW, ic = "bic"), Random_Walk = RW(NOW ~ drift()), Rede_Neural_AR = NNETAR(NOW, bootstrap = TRUE) ) |> forecast(h = "24 months") toc() # Seleção do melhor modelo Modelos |> accuracy(lnretNOW) |> arrange(RMSE) # Projeções fit <- lnretNOW |> model( Regr_Quebras = TSLM(NOW ~ trend(knots = c(2018, 2019, 2020))) ) sim <- fit |> generate(h = 30, times = 5, bootstrap = TRUE) # Plot lnretNOW |> filter_index("2025-01-01"~.) |> ggplot(aes(x = date)) + geom_line(aes(y = NOW)) + geom_line(aes(y = .sim, colour = as.factor(.rep)), data = sim) + labs(title="Retornos projetados da NOW", y="Log Returns") + guides(colour = "none") ``` ```{r} #| echo: false # Processamento para ORCL lnretORCL <- log_returns |> select(date, ORCL) |> as_tsibble(index = date) treino <- lnretORCL |> filter_index(~"2025-01-01") # Modelagem tic() Modelos_ORCL <- treino |> model( AjusteExp = ETS(ORCL ~ error("A") + trend("N") + season("N")), AjExp_aditivo = ETS(ORCL ~ error("A") + trend("A") + season("A")), AjExp_multiplicativo = ETS(ORCL ~ error("M") + trend("A") + season("M")), Croston = CROSTON(ORCL), HoltWinters = ETS(ORCL ~ error("M") + trend("Ad") + season("M")), Holt = ETS(ORCL ~ error("A") + trend("A") + season("N")), HoltAmort = ETS(ORCL ~ error("A") + trend("Ad", phi = 0.9) + season("N")), Regr_Comp = TSLM(ORCL ~ trend() + season()), Regr_Harmonica = TSLM(ORCL ~ trend() + fourier(K = 2)), Regr_Quebras = TSLM(ORCL ~ trend(knots = c(2018, 2019, 2020))), Snaive = SNAIVE(ORCL), Naive = NAIVE(ORCL), Media_Movel = ARIMA(ORCL ~ pdq(0,0,1)), autoARIMA = ARIMA(ORCL, stepwise = FALSE, approx = FALSE), autoARIMA_saz = ARIMA(ORCL, stepwise = FALSE, approx = FALSE, seasonal = TRUE), ARIMA_saz_012011 = ARIMA(ORCL ~ pdq(0,1,2) + PDQ(0,1,1)), ARIMA_saz_210011 = ARIMA(ORCL ~ pdq(2,1,0) + PDQ(0,1,1)), ARIMA_saz_0301012 = ARIMA(ORCL ~ 0 + pdq(3,0,1) + PDQ(0,1,2)), ARIMA_quad = ARIMA(ORCL ~ I(trend()^2)), ARIMA_determ = ARIMA(ORCL ~ 1 + trend() + pdq(d = 0)), ARIMA_estocastico = ARIMA(ORCL ~ pdq(d = 1)), Regr_Harm_dinamica = ARIMA(ORCL ~ fourier(K=2) + PDQ(0,0,0)), Regr_Harm_Din_MultSaz = ARIMA(ORCL ~ PDQ(0, 0, 0) + pdq(d = 0) + fourier(period = 7*30, K = 10) + fourier(period = 7*30, K = 5)), Regr_Harm_Din_Saz = ARIMA(ORCL ~ PDQ(0, 0, 0) + pdq(d = 0) + fourier(period = "month", K = 10) + fourier(period = "year", K = 2)), Modelo_VAR = VAR(ORCL, ic = "bic"), Random_Walk = RW(ORCL ~ drift()), Rede_Neural_AR = NNETAR(ORCL, bootstrap = TRUE) ) |> forecast(h = "24 months") toc() # Projeções fit_ORCL <- lnretORCL |> model( Regr_Quebras = TSLM(ORCL ~ trend(knots = c(2018, 2019, 2020))) # Faltava um parêntese aqui ) sim_ORCL <- fit_ORCL |> generate(h = 30, times = 5, bootstrap = TRUE) # Plot lnretORCL |> filter_index("2025-01-01"~.) |> ggplot(aes(x = date)) + geom_line(aes(y = ORCL)) + geom_line(aes(y = .sim, colour = as.factor(.rep)), data = sim) + labs(title="Retornos projetados da ORCL", y="Log Returns") + guides(colour = "none") ``` ```{r} #| echo: false # Processamento para IBM lnretIBM <- log_returns |> select(date, IBM) |> as_tsibble(index = date) treino <- lnretIBM |> filter_index(~"2025-01-01") # Modelagem tic() Modelos_IBM <- treino |> model( AjusteExp = ETS(IBM ~ error("A") + trend("N") + season("N")), AjExp_aditivo = ETS(IBM ~ error("A") + trend("A") + season("A")), AjExp_multiplicativo = ETS(IBM ~ error("M") + trend("A") + season("M")), Croston = CROSTON(IBM), HoltWinters = ETS(IBM ~ error("M") + trend("Ad") + season("M")), Holt = ETS(IBM ~ error("A") + trend("A") + season("N")), HoltAmort = ETS(IBM ~ error("A") + trend("Ad", phi = 0.9) + season("N")), Regr_Comp = TSLM(IBM ~ trend() + season()), Regr_Harmonica = TSLM(IBM ~ trend() + fourier(K = 2)), Regr_Quebras = TSLM(IBM ~ trend(knots = c(2018, 2019, 2020))), Snaive = SNAIVE(IBM), Naive = NAIVE(IBM), Media_Movel = ARIMA(IBM ~ pdq(0,0,1)), autoARIMA = ARIMA(IBM, stepwise = FALSE, approx = FALSE), autoARIMA_saz = ARIMA(IBM, stepwise = FALSE, approx = FALSE, seasonal = TRUE), ARIMA_saz_012011 = ARIMA(IBM ~ pdq(0,1,2) + PDQ(0,1,1)), ARIMA_saz_210011 = ARIMA(IBM ~ pdq(2,1,0) + PDQ(0,1,1)), ARIMA_saz_0301012 = ARIMA(IBM ~ 0 + pdq(3,0,1) + PDQ(0,1,2)), ARIMA_quad = ARIMA(IBM ~ I(trend()^2)), ARIMA_determ = ARIMA(IBM ~ 1 + trend() + pdq(d = 0)), ARIMA_estocastico = ARIMA(IBM ~ pdq(d = 1)), Regr_Harm_dinamica = ARIMA(IBM ~ fourier(K=2) + PDQ(0,0,0)), Regr_Harm_Din_MultSaz = ARIMA(IBM ~ PDQ(0, 0, 0) + pdq(d = 0) + fourier(period = 7*30, K = 10) + fourier(period = 7*30, K = 5)), Regr_Harm_Din_Saz = ARIMA(IBM ~ PDQ(0, 0, 0) + pdq(d = 0) + fourier(period = "month", K = 10) + fourier(period = "year", K = 2)), Modelo_VAR = VAR(IBM, ic = "bic"), Random_Walk = RW(IBM ~ drift()), Rede_Neural_AR = NNETAR(IBM, bootstrap = TRUE) ) |> forecast(h = "24 months") toc() # Projeções fit_IBM <- lnretIBM |> model( Regr_Quebras = TSLM(IBM ~ trend(knots = c(2018, 2019, 2020)) ) ) sim_IBM <- fit_IBM |> generate(h = 30, times = 5, bootstrap = TRUE) # Plot lnretIBM |> filter_index("2025-01-01"~.) |> ggplot(aes(x = date)) + geom_line(aes(y = IBM)) + geom_line(aes(y = .sim, colour = as.factor(.rep)), data = sim_IBM) + labs(title="Retornos projetados da IBM", y="Log Returns") + guides(colour = "none") ``` ```{r} #| echo: false # Processamento para MSFT lnretMSFT <- log_returns |> select(date, MSFT) |> as_tsibble(index = date) treino <- lnretMSFT |> filter_index(~"2025-01-01") # Modelagem tic() Modelos_MSFT <- treino |> model( AjusteExp = ETS(MSFT ~ error("A") + trend("N") + season("N")), AjExp_aditivo = ETS(MSFT ~ error("A") + trend("A") + season("A")), AjExp_multiplicativo = ETS(MSFT ~ error("M") + trend("A") + season("M")), Croston = CROSTON(MSFT), HoltWinters = ETS(MSFT ~ error("M") + trend("Ad") + season("M")), Holt = ETS(MSFT ~ error("A") + trend("A") + season("N")), HoltAmort = ETS(MSFT ~ error("A") + trend("Ad", phi = 0.9) + season("N")), Regr_Comp = TSLM(MSFT ~ trend() + season()), Regr_Harmonica = TSLM(MSFT ~ trend() + fourier(K = 2)), Regr_Quebras = TSLM(MSFT ~ trend(knots = c(2018, 2019, 2020))), Snaive = SNAIVE(MSFT), Naive = NAIVE(MSFT), Media_Movel = ARIMA(MSFT ~ pdq(0,0,1)), autoARIMA = ARIMA(MSFT, stepwise = FALSE, approx = FALSE), autoARIMA_saz = ARIMA(MSFT, stepwise = FALSE, approx = FALSE, seasonal = TRUE), ARIMA_saz_012011 = ARIMA(MSFT ~ pdq(0,1,2) + PDQ(0,1,1)), ARIMA_saz_210011 = ARIMA(MSFT ~ pdq(2,1,0) + PDQ(0,1,1)), ARIMA_saz_0301012 = ARIMA(MSFT ~ 0 + pdq(3,0,1) + PDQ(0,1,2)), ARIMA_quad = ARIMA(MSFT ~ I(trend()^2)), ARIMA_determ = ARIMA(MSFT ~ 1 + trend() + pdq(d = 0)), ARIMA_estocastico = ARIMA(MSFT ~ pdq(d = 1)), Regr_Harm_dinamica = ARIMA(MSFT ~ fourier(K=2) + PDQ(0,0,0)), Regr_Harm_Din_MultSaz = ARIMA(MSFT ~ PDQ(0, 0, 0) + pdq(d = 0) + fourier(period = 7*30, K = 10) + fourier(period = 7*30, K = 5)), Regr_Harm_Din_Saz = ARIMA(MSFT ~ PDQ(0, 0, 0) + pdq(d = 0) + fourier(period = "month", K = 10) + fourier(period = "year", K = 2)), Modelo_VAR = VAR(MSFT, ic = "bic"), Random_Walk = RW(MSFT ~ drift()), Rede_Neural_AR = NNETAR(MSFT, bootstrap = TRUE) ) |> forecast(h = "24 months") toc() # Projeções fit_MSFT <- lnretMSFT |> model( Regr_Quebras = TSLM(MSFT ~ trend(knots = c(2018, 2019, 2020)) ) ) sim_MSFT <- fit_MSFT |> generate(h = 30, times = 5, bootstrap = TRUE) # Plot lnretMSFT |> filter_index("2025-01-01"~.) |> ggplot(aes(x = date)) + geom_line(aes(y = MSFT)) + geom_line(aes(y = .sim, colour = as.factor(.rep)), data = sim_MSFT) + labs(title="Retornos projetados da MSFT", y="Log Returns") + guides(colour = "none") ```